Method and system for improving the evaluation of an interaction between an analyte and a ligand using a biosensor

ABSTRACT

Methods and biosensor systems for improved evaluation of an interaction between an analyte in a fluid sample and a ligand immobilized on a sensor surface of a biosensor are provided. In one example, a method is provided which includes allowing a plurality of fluid samples to flow across a first sensor surface and a second sensor surface having a ligand immobilized thereon, where the fluid samples include a solvent (for example, an organic solvent with bulk effects such as DMSO) at known concentrations. The method further includes creating a data set for each fluid sample and forming a clean data set with outliers removed. Software for performing steps of methods disclosed and a computer readable medium for storing the software are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a filing under 35 U.S.C. 371 of internationalapplication number PCT/EP2016/073271, filed Sep. 29, 2016, which claimspriority to Great Britain application number GB1517279.4, filed Sep. 30,2015, the entire disclosure of each of which is hereby incorporated byreference.

TECHNICAL FIELD

The present invention relates to a method and system for improving theevaluation of an interaction between an analyte in a fluid sample and aligand immobilized on a sensor surface of a biosensor, and to softwarefor performing the steps of the method and a computer readable mediumfor storing the software.

BACKGROUND

Analytical sensor systems that can monitor interactions betweenmolecules, such as biomolecules, in real time are gaining increasinginterest. These systems are often based on optical biosensors andusually referred to as interaction analysis sensors or biospecificinteraction analysis sensors. A representative such biosensor system isthe BIACORE® instrumentation sold by GE Healthcare, which uses surfaceplasmon resonance (SPR) for detecting interactions between molecules ina sample and molecular structures immobilized on a sensing surface. Assample is passed over the sensor surface, the progress of bindingdirectly reflects the rate at which the interaction occurs. Injection ofsample is followed by a buffer flow during which the detector responsereflects the rate of dissociation of the complex on the surface. Atypical output from the BIACORE® system is a graph or curve describingchange in refractive index at the sensor surface and thereby theprogress of the molecular interaction with time, including anassociation phase part and a dissociation phase part. This graph orcurve, which is usually displayed on a computer screen, is oftenreferred to as a binding curve or “sensorgram”.

With the BIACORE® system (and analogous sensor systems) it is thuspossible to determine a plurality of interaction parameters for themolecules used as ligand and analyte. These parameters include kineticrate constants for binding (association) and dissociation in themolecular interaction as well as the affinity for the surfaceinteraction. The association rate constant (k_(a)) and the dissociationrate constant (k_(d)) can be obtained by fitting the resulting kineticdata for a number of different sample analyte concentrations tomathematical descriptions of interaction models in the form ofdifferential equations. The affinity (expressed as the affinity constantK_(A) or the dissociation constant K_(D)) can be calculated from theassociation and dissociation rate constants.

Several factors may cause deviations in refractive index other than theintended interaction of molecules, most notably the solvent contained inthe sample passed over the sensor surface. Solvent correction adjustsreference-subtracted responses for small artefacts that can beintroduced by variations in the bulk refractive index between samples.The correction is generally required when variations in the bulkrefractive index are of the same order of magnitude as the response:this situation arises commonly in work with small organic biomoleculesthat give intrinsically low response values and that often requireorganic solvents such as dimethyl sulfoxide (DMSO) to maintainsolubility.

The need for solvent correction arises because subtraction of thereference response does not exactly eliminate the contribution of thebulk solution to the measured response. Bulk solution is excluded fromthe volume occupied by ligand on the active surface, so that the bulkcontribution to the response on the active surface is slightly smallerthan that on the reference surface. As long as the refractive index ofthe samples is constant, this excluded volume effect introduces aconstant error in reference subtraction which may be ignored forpractical purposes. However, if the refractive index of the samplesvaries, the magnitude of the excluded volume effect will also vary.Reference measurements are therefore performed at regular intervals bypassing solvent samples containing the solvent at different knownconcentrations over the sensor surface and creating reference-subtractedresponse values. The quality of these measurements may be difficult toassess, however, and the results may be subjected to drift over time,making it difficult to achieve high quality interaction data.

There is therefore generally a need for improved methods to increase thequality when evaluating the interaction between molecules in a sampleand molecules immobilized on a sensor surface.

DISCLOSURE OF THE INVENTION

The object of the invention is to provide a new method and biosensorsystem for improving the evaluation of an interaction between an analytein a fluid sample and a ligand immobilized on a sensor surface of abiosensor, which method and biosensor system overcomes one or moredrawbacks of the prior art.

One of the benefits of the invention is that the reference values may beassessed and outliers in the resulting data set may be identified andremoved. The remaining values can be used with the solvent correctionmethod or another similar method to improve the quality of results forthe interaction between molecules obtained using surface plasmonresonance.

Many additional benefits of the invention will become readily apparentto the person skilled in the art in view of the detailed descriptionbelow.

DRAWINGS

The invention will now be described in more detail with reference to theappended drawings, wherein:

FIG. 1 is a schematic side view of a biosensor system based on SPR;

FIG. 2 is a representative sensorgram where the binding curve hasvisible association and dissociation phases;

FIG. 3 shows steps of the method according to a preferred embodiment ofthe invention;

FIGS. 4a-4h disclose eight sample curves that were used to test themethod

FIG. 5 shows a biosensor instrument according to an embodiment of theinvention.

DETAILED DESCRIPTION

As mentioned above, the present invention relates to a method and abiosensor system for evaluation of an interaction between an analyte ina fluid sample and a ligand immobilized on a sensor surface of abiosensor.

Typically, the experimental binding data is obtained by sensor-basedtechnology, which studies the molecular interactions and presents theresults in real time as the interactions progress. Before describing thepresent invention in more detail, however, the general context in whichthe invention is intended to be used will be described.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by a person skilled in theart related to this invention. Also, the singular forms “a”, “an”, and“the” are meant to include plural reference unless it is statedotherwise.

All publications, patent applications, patents, and other referencesmentioned herein are incorporated by reference in their entirety.

Chemical sensors or biosensors are typically based on label-freetechniques, detecting a change in a property of a sensor surface, suchas e.g. mass, refractive index, or thickness for the immobilized layer,but there are also sensors relying on some kind of labelling. Typicalsensor detection techniques include, but are not limited to, massdetection methods, such as optical, thermo-optical and piezoelectric oracoustic wave methods (including e.g. surface acoustic wave (SAW) andquartz crystal microbalance (QCM) methods), and electrochemical methods,such as potentiometric, conductometric, amperometric andcapacitance/impedance methods. With regard to optical detection methods,representative methods include those that detect mass surfaceconcentration, such as reflection-optical methods, including bothexternal and internal reflection methods, which are angle, wavelength,polarization, or phase resolved, for example evanescent waveellipsometry and evanescent wave spectroscopy (EWS, or InternalReflection Spectroscopy), both of which may include evanescent fieldenhancement via surface plasmon resonance (SPR), Brewster anglerefractometry, critical angle refractometry, frustrated total reflection(FTR), scattered total internal reflection (STIR) (which may includescatter enhancing labels), optical wave guide sensors; externalreflection imaging, evanescent wave-based imaging such as critical angleresolved imaging, Brewster angle resolved imaging, SPR-angle resolvedimaging, and the like. Further, photometric and imaging/microscopymethods, “per se” or combined with reflection methods, based on forexample surface enhanced Raman spectroscopy (SERS), surface enhancedresonance Raman spectroscopy (SERRS), evanescent wave fluorescence(TIRF) and phosphorescence may be mentioned, as well as waveguideinterferometers (e.g. Bio-Layer Interferometry as implemented byForteBio®), waveguide leaky mode spectroscopy, reflective interferencespectroscopy (RIfS), transmission interferometry, holographicspectroscopy, and atomic force microscopy (AFR). Commercially availablebiosensors include the afore-mentioned BIACORE® system instruments,manufactured and marketed by GE Healthcare, which are based on surfaceplasmon resonance (SPR) and permit monitoring of surface bindinginteractions in real time between a bound ligand and an analyte ofinterest. In this context, “ligand” is a molecule that has a known orunknown affinity for a given analyte and includes any capturing orcatching agent immobilized on the surface, whereas “analyte” includesany specific binding partner thereto.

While in the detailed description, the present invention is illustratedin the context of SPR spectroscopy, and more particularly the BIACORE®system, it is to be understood that the present invention is not limitedto this detection method. Rather, any affinity-based detection methodwhere an analyte binds to a ligand immobilized on a sensing surface maybe employed, provided that a change at the sensing surface can bemeasured which is quantitatively indicative of binding of the analyte tothe immobilized ligand thereon.

The phenomenon of SPR is well known, suffice it to say that SPR ariseswhen light is reflected under certain conditions at the interfacebetween two media of different refractive indices, and the interface iscoated by a metal film, typically silver or gold. In the BIACORE®instruments, the media are the sample and the glass of a sensor chip,which is contacted with the sample by a micro fluidic flow system. Themetal film is a thin layer of gold on the chip surface. SPR causes areduction in the intensity of the reflected light at a specific angle ofreflection. This angle of minimum reflected light intensity varies withthe refractive index close to the surface on the side opposite from thereflected light, in the BIACORE® system the sample side.

A schematic illustration of the BIACORE® system is shown in FIG. 1.Sensor chip 1 has a gold film 2 supporting capturing molecules (ligands)3, e.g. antibodies, exposed to a sample flow with analytes 4, e.g. anantigen, through a flow channel 5. Monochromatic p-polarized light 6from a light source 7 (LED) is coupled by a prism 8 to the glass/metalinterface 9 where the light is totally reflected. The intensity of thereflected light beam 10 is detected by an optical detection unit 11(photodetector array).

A detailed discussion of the technical aspects of the BIACORE®instruments and the phenomenon of SPR may be found in U.S. Pat. No.5,313,264. More detailed information on matrix coatings for biosensorsensing surfaces is given in, for example, U.S. Pat. Nos. 5,242,828 and5,436,161. In addition, a detailed discussion of the technical aspectsof the biosensor chips used in connection with the BIACORE® instrumentsmay be found in U.S. Pat. No. 5,492,840. When molecules in the samplebind to the capturing molecules on the sensor chip surface, theconcentration, and therefore the refractive index at the surface changesand an SPR response is detected. Plotting the response against timeduring the course of an interaction will provide a quantitative measureof the progress of the interaction. Such a plot, or kinetic or curve(binding isotherm), is usually called binding curve or sensorgram, alsosometimes referred to in the art as “affinity trace” or “affmogram”. Inthe BIACORE® system, the SPR response values are expressed in resonanceunits (RU). One RU represents a change of 0.0001° in the angle ofminimum reflected light intensity, which for most proteins and other biomolecules correspond to a change in concentration of about 1pg/mm{circumflex over ( )} the sensor surface. As sample containing ananalyte contacts the sensor surface, the capturing molecule (ligand)bound to the sensor surface interacts with the analyte in a stepreferred to as “association.” This step is indicated in the bindingcurve by an increase in RU as the sample is initially brought intocontact with the sensor surface. Conversely, “dissociation” normallyoccurs when the sample flow is replaced by, for example, a buffer flow.This step is indicated in the binding curve by a drop in RU over time asanalyte dissociates from the surface-bound ligand. A representativebinding curve (sensorgram) for a reversible interaction at the sensorchip surface is presented in FIG. 2, the sensing surface having animmobilized capturing molecule, or ligand, for example an antibody,interacting with a binding partner therefore, or analyte, in a sample.The binding curves produced by biosensor systems based on otherdetection principles mentioned above will have a similar appearance. Thevertical axis (y-axis) indicates the response (here in resonance units,RU) and the horizontal axis (x-axis) indicates the time (here inseconds). Below the horizontal axis, the acquisition cycle for acquiringa binding curve is schematically disclosed divided in different timesections where the sensor surface is put into contact with differentfluids. Initially, from to t1 to t2, buffer (B) is passed over thesensing surface giving the baseline response 1 in the binding curve.Then, during from t2 to t3, the sensor surface is contacted with asample containing an analyte at a concentration Ci whereby an increasein signal is observed due to binding of the analyte. This part 2 of thebinding curve is usually referred to as the “association phase”.Eventually, a steady state condition is reached at or near the end ofthe association phase where the resonance signal plateaus at 3 (thisstate may, however, not always be achieved). It is to be noted thatherein the term “steady state” is used synonymously with the term“equilibrium” (in other contexts the term “equilibrium” may be reservedto describe the ideal interaction model, since in practice binding couldbe constant over time even if a system is not in equilibrium). At theend of the association phase, at t3, the sample is often replaced with acontinuous flow of buffer (B) and a decrease in signal reflects thedissociation, or release, of analyte from the surface. This part 4 ofthe binding curve is usually referred to as the “dissociation phase”.The analysis is optionally ended by a regeneration step, at t4, where asolution capable of removing bound analyte from the surface (R), while(ideally) maintaining the activity of the ligand, is injected over thesensor surface. This is indicated in part of the sensorgram. At t₅injection of buffer (B) restores the baseline I and the surface is nowready for a new analysis. In some situations it may be convenient toomit the regeneration step V and initiate a new injection cycle withoutregeneration. Examples of such situations comprise concentration seriesof the same analyte, screening of analytes with a sufficiently highdissociation rate to allow essentially complete dissociation, etc. Fromthe profiles of the association and dissociation phases II and IV,respectively, information regarding the binding and dissociationkinetics is obtained, and the height of the binding curve at IIIrepresents affinity (the response resulting from an interaction beingrelated to the change in mass concentration on the surface).

Solvent correction (SC) is a procedure that corrects forsample-to-sample variations in bulk effects, which can introducesignificant reference subtraction errors. These effects arise becausereference and ligand surfaces are structurally different. Bulk solutionis excluded from the volume occupied by ligand molecules on the ligandsurface, effectively reducing potential bulk effects. Correction oftenbecomes important for samples including small molecules stored inorganic solvents such as DMSO, which can dramatically affect therefractive index of the solution. The approach of SC is to measure theresponse on both ligand and reference surface during injections of blanksamples containing a range of DMSO concentrations. Such runs areperformed cyclically in between sample runs to correct for any drifts inthe response. For each SC run, the reference-subtracted response on theligand is then plotted against the reference response, and a quadraticpolynomial is fit to the data. Each sample measurement is corrected bythe factor obtained by measuring the reference response during thesample injection and reading off the SC curve what ligand-referencedifference this corresponds to.

Thus, certain factors must be considered when assessing the quality ofdata gathered by the Solvent Correction method. Specifically, χ², is ameasure of the statistical error of the measurements (detaileddefinitions and description of terminology are found below). A large χ²can indicate that outliers, data points which do not follow the generaltrend of the data, are present. In addition, the intersection of the SCcurve with the y-axis, Y₀, can be used as a quality indicator. Ideally,Y₀ should be close to zero. How big a Y₀ deviation from zero should beconsidered significantly large is however difficult to quantify at thestage at which Solvent Correction (SC) is performed.

The regression analysis technique currently utilized in the Biacore 4000SC procedure is linear least squares, using a quadratic polynomialmodel:y(x)=ax ² +bx+c,where c=Y₀. The number of regression parameters, p, thus adds up to 3. Anormally distributed error term, responsible for the statisticaluncertainties of the measurements, should also be added to thisexpression. The mean of this error should be zero, but moreinterestingly, the variance, χ (sometimes also referred to as MSE, “meansquare error”) can be estimated from a data set (x_(i), y_(i)), i=1, . .. , n, as

$\chi^{2} = {\sum\limits_{i = 1}^{n}{e_{i}^{2}/{\left( {n - p} \right).}}}$The e_(i) are residuals defined by e_(i)=y_(i)−f_(i), wheref_(i)=f(x_(i)) is a prediction of y(x_(i)) made by the regression curvef(x). The residuals and χ² measure deviations in the y-direction. Thecorresponding variables for the x-direction are the leverages, h_(i).These are defined as the diagonal elements of the so called “Hatmatrix”, H, given byH=X(X ^(T) X)⁻¹ X ^(T),where X is the n×p so called design matrix of the regression.Specifically, for quadratic regression, which is the most relevant here,

$X = {\begin{bmatrix}1 & x_{1} & x_{1}^{2} \\\vdots & \vdots & \vdots \\1 & x_{n} & x_{n}^{2}\end{bmatrix}.}$This means we can write the leverages ash _(i) =X _(i)(X ^(T) X)⁻¹ X _(i) ^(T).where X_(i) is the ith row vector of X, corresponding to observation i.A high leverage for a certain data point (note: since here, 0≤h_(i)≤1,“high” means close to 1) means that it is located far away from the mainmass of data in the x-direction. As the name suggests, high-leveragepoints force the regression curve to pass by very close to them.

An outlier is here defined as an observation that does not fit with thepattern displayed by the majority of the remaining observations. Thepresence of outliers in the data set used for SC would introducedisturbance in the results of the interaction between analyte andligand. For the purpose of the invention it is to be distinguishedbetween two types of outliers: large residual points and bad leveragepoints. Large residual points are outliers only in the y-direction,while bad leverage points are outliers in both directions. In addition,there are good leverage points, which are only outliers in thex-direction.

It is possible to attack the problem of outliers in at least twodifferent ways. Either one can 1) use a outlier-resistant robustregression technique that pays less attention to extreme points from thestart, or, 2) one applies least squares (LS), and from there tries todetect suspicious points by the use of some regression diagnostic. Thissection focuses on approach 2).

To find large residual points it is natural to look at the residuale_(i) of each point, scaled (divided) by an estimate of the standarddeviation of the residual, which is a function of the leverage h_(i).This measure is called the internally Studentized residual and is givenby

$t_{i}^{int} = {\frac{e_{i}}{\chi\sqrt{1 - h_{i}}}.}$

In addition, many popular regression diagnostics are based on a“one-deletion” procedure, the question being: how does the deletion ofone single observation affect the regression? Removing an outlier shouldin general greatly impact the regression. An example of such adiagnostic is the externally Studentized residual, defined by

${t_{i}^{ext} = \frac{e_{i}}{\chi_{(i)}\sqrt{1 - h_{i}}}},$where a subscript (i) will always indicate that the calculations havebeen made using the data set with point i deleted. Basically t_(i)^(ext) is the residual scaled by its standard deviation, but with χreplaced by its one-deletion partner. Under the assumption ofindependent, Gaussian errors (which will always be assumed), thisstatistic follows a t-distribution with (n−p−1) degrees of freedom.In addition to such residual measures, several so called “influence”measures may be used, which attempt to capture how much power a certainpoint has over the regression. One example is DFFITS, given by

${{DFFITS}_{i} = \frac{{f_{i} - f_{i{(i)}}}}{\chi_{(i)}\sqrt{h_{i}}}},$where f_(i(i)) is the regression function with point i deleted,evaluated at x=x_(i). It can be shown that DFFITS is simply related tot^(ext) _(i) by

${{DFFITS}_{i} = {t_{i}^{ext}\sqrt{\frac{h_{i}}{1 - h_{i}}}}},$i.e., a large Studentized residual combined with high leverage aretypical characteristics of an influential point.

After having reviewed one-deletion diagnostics, it is natural toconsider the reversed situation of one-inclusion diagnostics. Given aninitial data set, with what certainty can we predict the value of a newobservation y_(i) using a regression based on these initialobservations? A statistic similar to t_(i) ^(ext) can here be useful,namely the prediction residual t_(i) ^(pred), defined by

${t_{i}^{pred} = \frac{e_{i}}{\chi\sqrt{1 + h_{i}}}},$where h_(i) is a generalization of the leverage defined previously. Thedefinition of h_(i) remains the same, except for the important fact thatfor this case, the row vector X_(i) will not be a row of the matrix ofregression, X, since X only contains the rows corresponding the initialand not the “new” observation (also, when X_(i) is not a row of X,h_(i)>1 is possible). t_(i) ^(pred) has a t-distribution with (n−p)degrees of freedom.

The method and system according to the invention will now be describedin more detail, followed by an experiment to evaluate the method using anumber of curves obtained using the solvent correction method. It is tobe noted, however, that the method may also be used with data obtainedthrough other methods and that the embodiments described below are notto be seen as limiting the invention. The preferred embodiment isdescribed using the Biacore® 4000 system to obtain the results, but itis to be noted that other systems may of course also be used.

Thus, according to a preferred embodiment of the present invention abiosensor system is provided with a first sensor surface and a secondsensor surface on which a ligand is immobilized. The first sensorsurface is provided without any immobilized molecules on its surface. Aplurality of fluid samples are allowed to flow across the first andsecond sensor surface and changes in refractive index are measured foreach sample. The fluid samples comprise a solvent, preferably an organicsolvent such as DMSO that is also used for containing the analyte usedfor interaction with the ligand, and the solvent is present at aplurality of different known concentrations.

For each fluid sample a reference value and a reference-subtractedresponse value are created, where the reference value is the measuredresponse at the second sensor surface and the reference-subtractedresponse value is the response at the second sensor surface subtractedby the response at the first sensor surface. A data set is created withthe reference value and the reference-subtracted response value forminga point for each fluid sample.

From the data set a reliable set is chosen comprising at least foursamples and the reference value for each point is plotted against thereference-subtracted value and a curve fitted to them using any suitablemethod such as a polynomial fitting for instance. The remaining pointsin the data set are tested against the reliable set using the stepsa)-f) as described further below to determine if any of them areoutliers and should be removed from the set to increase the quality ofresults. For each point the following steps a)-f) are thereforeperformed, and the steps are also shown by FIG. 3.

-   -   a) calculating the leverages h_(i).    -   b) labelling points with h_(i)>h_(i) ^(cut) as outliers. If the        number of outliers, n_(o), is less than n_(o) ^(max)=min(n−p−1,        floor((n−1)/2)), continue; otherwise, go to step f) below,    -   c) forming a clean set with any outliers removed and calculating        the n^(clean) Studentized residuals t_(i) ^(ext) using a        regression based on this clean set, where n^(clean) is the size        of the clean set,    -   d) labelling points with t_(i) ^(ext)>t(α/(2n^(clean)),        n^(clean)−p−1) as outliers and if n_(o)<n_(o) ^(max), continue;        otherwise, go to step f) below,    -   e) forming a clean set with outliers removed again, if outliers        were found in the previous step d). If χ²>χ² _(cut), where χ² is        calculated from regression of the clean set, calculating the        n^(clean) Studentized residuals t_(i) ^(ext) for all points in        the clean set and labelling outliers just as was done in the        previous step d),    -   f) if any high-leverage outliers were detected in step b) and        n_(o)≤n_(o) ^(max), calculating t_(i) ^(pred) for these        high-leverage points using a regression based on the clean,        outlier-free set, and removing the outlier label for this points        if t_(i) ^(pred)<t(α/2, n^(clean)−p).

The heart of the algorithm is the Studentized residual t-test of stepsc) and d). Here, a so called Bonferroni correction of the significancelevel a is used to account for the fact that actually n^(clean)significance tests are being performed, increasing the probability offinding something “abnormal” than if only one randomly chosen point weretested. In order to prevent high-leverage points, which may distort theregression curve from disturbing these tests they are temporarilylabeled as outliers during steps a)-b) and removed from the clean set.In step f) each of these points is classified as a good leverage points(not outlier) or a bad leverage points (outlier) based on whether itfalls within the prediction interval of the “clean” regression or not,at a significance level a that may be selected as desired.

A common problem of regression is the effect of “masking”, that is, whenthe presence of one outlier can help to hide, i.e. mask, the presence ofanother outlier. Step e) serves to solve this problem. If any outlierswere detected in step d), and the resulting χ² for the remaining set ofpoints is still considered large, i.e., χ²>×² _(cut), anotherlarge-residual t-test is performed. This cut-off is included to avoidexcessive “trimming” of the curves, and so that another residual test isonly performed for certain cases. χ² _(cut) could for instance be set toa value that is large as compared to the current set of SC curves. Oneoutlier-robust way of doing this is to setχ_(cut) ²=χ_(rel) ²=med(χ₂ ^(j))+mMAD(χ_(j) ²).where χ_(j) ² is χ² of the jth SC curve included in the SC analysis (ascalculated from the full data set), “med” denotes the median, and m is anon-negative integer determining how far away from the median is to beconsidered too large. MAD is the mean absolute deviation, a robustvariant of the usual standard deviation, defined byMAD(χ_(j) ²)=med(χ_(j) ²−med(χ_(j) ²))

When using χ_(rel) ² it may be that a set of relatively small χ_(j) ²'scould give a quite small χ² _(cut) (e.g. <1 RU²). Furthermore, whereonly a small number of curves are included in the analysis, the resultsmay not be statistically significant. Hence, an alternative is to set χ²_(cut) to a fixed constant χ₀ ², say ˜10 RU², making sure that a maskingtest will never be performed if χ²<χ₀ ². A potential problem with onlyusing χ₀ ² is that a set of relatively large χ_(j) ²'s could lead tounwanted and unnecessary masking tests. These alternatives may thereforebe combined by settingχ² _(cut)=max(χ₀ ²,χ_(ref) ²)if there are sufficiently many curves (say, 5) for the relative measureto be reasonable, and setting χ² _(cut)=χ₀ ² otherwise.In order to further improve the method with regard to detectingoutliers, an additional step may be added, namelyg) calculating the DFFITS for each point and labeling points withDFFITS_(i)>f(t(α/(2n^(clean)), n^(clean)−p−l), h_(i) ^(cut)) as outliers. If the number of outliers, n_(o), is lessthan n_(o) ^(max)=min(n−p−1, floor((n−1)/2)), continue; otherwise, go tostep f).

This step is preferably inserted at the beginning of the method, beforeor after any of the steps a) and b) and provide an additional labellingof data points suspected of being outliers. Furthermore, data that showdifferent slope inside a data point compared to other points have beenshown in studies to be potential outliers. A point solvent correctionvalue is calculated from a baseline in the sensorgram and a specificpoint area inside the solvent correction inject. The point value iscalculated as the average of the specific point area−baseline.

An additional procedure can be used with the preferred embodiment of thepresent invention to further identify outliers through the steps of

-   -   i) Calculating a slope for all point area data inside each        point.    -   ii) Calculating a difference between average and median of the        data inside each point.    -   iii) Calculating a difference between the slope calculated in        step i) and median of all slopes calculated in step i).    -   iv) Sorting the data from step iii).    -   v) Determining a clean set of the sorted data from step iv) by        removing data with largest difference to median    -   vi) Using the clean set to calculate normal difference to median    -   vii) Classifying a point as outlier if difference against median        is larger than a first predetermined value and data from        step ii) is larger than a second predetermined value.

By applying these steps a clean set is also created and can serve asinput to the method steps a)-f) or a)-g). Preferably, said firstpredetermined value is 20 times the value determined in step vi) and thesaid second predetermined value is 1 RU.

Experiment

The method according to the present invention will now be evaluated byusing the steps a)-f) on 8 different SC curves obtained through theSolvent Correction (SC) method as described above. The curves themselvesare denoted by numbers 1-8 and shown by FIG. 4a-4h . All the curves haveχ²>1 RU², since this is a reasonable cut-off to choose as a “goodenough” χ².

The settings of the parameters from the method steps a)-f) when runningthis test were: h_(i) ^(cut)=0.85, χ₀ ²=10 RU² and m=5. The two lowersignificance levels, 1% and 5%, are applied in turn.

The results are summarized in table 1 below. Here each curve is listedwith its χ², and for each significance level, the indices of the points(as defined in the figures of the curves in FIG. 4a-4h ) which wereidentified as outliers by the method. The right-most column contains theindices of the “true” outliers. A ‘-’ denotes that no outliers weredetected for that significance level and method.

The final row of table 1 lists the number of detected true outliers forthe test of the corresponding column. This number provides a roughmeasure of how well the different significance levels are doing.Specifically, it is seen that the stricter 1% level makes the methodmiss more or less half of the apparent outliers, while the 5% levelallows the method to find almost all of them. All of the detections madein this experiment lead to a dramatic relative decrease in χ² afterremoval of the proposed outliers. Of all tests which lead to outlierdetections, the test resulting in the minimum relative decreasenonetheless decreased χ² by 85%, while the average decrease was by 95%.Thus, according to this χ²-measure, all suspicions are well-grounded. Inreality however, absolute measures are important. To facilitate theevaluation of the method in terms of absolute RUs, FIGS. 5a-5h contain abar chart for each curve, with the original χ² value and the resultingχ2 reductions after outlier removal for each significance level.

TABLE 1 Results of the experiment on 8 different curves. χ² “True” Curve(RU²) α = 1% α = 5% outliers 1 128.8 6 6 6 2 1.988 — 1 1 3 4.101 — 1 1 41.791 — 3 3 5 23.43 — — — 6 1.491 — 2 — 7 10.08 6 6 6 8 7.338 — 8 8

The curves and the results in Table 1 can further be described asfollows:

Curve 1 (FIG. 4a ): Point 6 is an obvious outlier, and the methoddetects this point at both a levels.

Curve 2 (FIG. 4b ): The method detects that point 1 is an outlier on the5% level. Even though it looks like a fine fit to the eye, excludingthis point actually leads to a significantly lower χ² of ˜0.16 RU²,which is essentially what triggers the method to declare the presence ofoutliers. Deleting point 1 gives the curve a χ²<0.6 RU².Curve 3 (FIG. 4c ): For this curve it is quite clear that point 1 is anoutlier and it is identified as such on the 5% level but not on the 1%level.Curve 4 (FIG. 4d ): Point 3 is an outlier. Indications such as a steepreport point region are found upon inspection of the sensorgram. Themethod successfully detects this point for α=5%.Curve 5 (FIG. 4e ): This curve contains no obvious outliers and the sameconclusion is drawn by both outlier tests.Curve 6 (FIG. 4f ): The method comes to the conclusion that point 2 is a5% level outlier, even though it is not apparent to the naked eye.Deleting it leads to a χ² decrease from 1.491 to 0.3323 RU².Curve 7 (FIG. 4g ): This curve exhibits a distinct outlier, which isdetected already at α=1%.Curve 8 (FIG. 4h ): Again, the method identifies the outlier as pointnumber 8.

It can therefore be concluded that the method according to the presentinvention is suitable for identifying outliers in a clear majority ofthe curves on which it was tested, and that a higher level of α=5% givesimproved results compared with a lower level of 1%.

The steps of the method may be performed by software running in aprocessor, and said software may also be stored in a computer readablemedium. The term computer readable medium as used herein is to beunderstood as any medium suitable for storing data for access by acomputer or similar tool, such as an RAM, a memory stick, a compactdisc, etc.

The invention has been described above with reference to the solventcorrection method, but it is to be noted that the method according tothe invention can also be used in other situations, such as whendetermining affinity for example.

FIG. 5 shows a biosensor instrument 100 according to the invention,including a biosensor 101 which can be constructed as shown in FIG. 1and operated in a manner described above with reference to FIG. 1,except that two parallel sensor surfaces 102A and 102B are used in thisembodiment, each of which has the same construction as described above,although they are served by one light source 107 and light intensity ismeasured by different parts of the same light detector 111. A processor112 for carrying out the method described above receives signals fromlight detector 111 derived from both sensor surfaces 102A and 102Boperable in a similar way to the detector 11 shown in FIG. 1. Theprocessor controls the flow of sample fluids to each sensor surface, atpump 116 and can read and write data form and to a memory 114. In thisway the instrument can operate as claimed by means of software runningin the processor 112.

The invention claimed is:
 1. A method for improved evaluation of aninteraction between an analyte in a fluid sample and a ligandimmobilized on a sensor surface of a biosensor, comprising the steps of:providing a first sensor surface, and providing a second sensor surfacehaving a ligand immobilized thereon, allowing a plurality of fluidsamples to flow across said first and said second sensor surface whereinthe fluid samples comprise a solvent at known concentration, measuringchanges of refractive index at the first and second sensor surfaceduring the flow of each fluid sample, determining a response value and areference-subtracted response value for each fluid sample based on saidchanges and creating a data set comprising said values, each fluidsample forming a point in the data set, selecting a reliable setcomprising at least five samples from the data set, plotting theresponse value against the reference-subtracted response value for thereliable set and fitting a curve to them, and further comprising stepsa)-f) below, said steps being performed in alphabetical order for everyother fluid sample in the data set a) calculating leverages h_(i), b)labelling points with h_(i)>h_(i) ^(cut) as outliers, and if the numberof outliers, n_(o), is less than n_(o) ^(max)=min(n−p−1,floor((n−1)/2)), continue; otherwise, go to step f) below, c) forming aclean set with outliers removed and calculating n^(clean) Studentizedresiduals t_(i) ^(ext) using a regression based on this clean set, wheren^(clean) represents size of the clean set, d) labelling points witht_(i) ^(ext)>t(a/(2n^(clean)), n^(clean)−p−1) as outliers, and ifn_(o)<n_(o) ^(max), continue; otherwise, go to step f) below, e) forminga clean set with outliers removed again, if outliers were found inprevious step d); if χ²>χ² _(cut), where χ² is calculated fromregression of the clean set, calculating the n^(clean) Studentizedresiduals t_(i) ^(ext) for all points in the clean set and labellingoutliers just as was done in previous step d), f) if any high-leverageoutliers were detected in step b) and n_(o)<n_(o) ^(max), calculatingt_(i) ^(pred) for these high-leverage points using a regression based onthe clean, outlier-free set, and removing the outlier label for thesepoints if t^(red)<t(α/2, n^(clean)−p).
 2. The method according to claim1, wherein the method further comprises the steps of: g) calculating aninfluence measure, referred to as DFFITS, for each point and labelingpoints with DFFITS_(i)>f(t(α/(2n^(clean)), n^(clean)−p−1), h_(i) ^(cut))as outliers; if the number of outliers, n_(o), is less than n_(o)^(max)=min(n−p−1, floor((n−1)/2)), continue; otherwise, go to step f),and wherein said step g) is performed before or after any of the stepsa) and b).
 3. The method according to claim 1, wherein the methodfurther comprises determining a clean set by i) calculating a slope forall point area data inside each point, ii) calculating a differencebetween average and median of the data inside each point, iii)calculating a difference between the slope calculated in step i) andmedian of all slopes calculated in step i), iv) sorting the data fromstep iii), v) determining a clean set of the sorted data from step iv)by removing data with largest difference to median, vi) using the cleanset to calculate normal difference to median, vii) classifying a pointas outlier if difference against median is larger than a firstpredetermined value and data from step ii) is larger than a secondpredetermined value.
 4. The method according to claim 3, wherein saidfirst predetermined value is 20 times the value determined in step vi).5. The method according to claim 3, wherein said second predeterminedvalue is 1 resonance units.
 6. The method according to claim 1, whereinχ²=max(χ_(o) ², χ² _(rel)).
 7. The method according to claim 1, whereinthe solvent is an organic solvent, preferably dimethyl sulfoxide.
 8. Abiosensor system, comprising a processor, for improved evaluation of aninteraction between an analyte in a fluid sample and a ligandimmobilized on a sensor surface of a biosensor, characterized in beingarranged to perform the steps of the method according to claim
 1. 9. Abiosensor instrument for evaluation of an interaction between an analytein a fluid sample and a ligand immobilized on a sensor surface of abiosensor, the instrument having a biosensor including a first sensorsurface, and a second sensor surface having a ligand immobilizedthereon, means for causing a plurality of fluid samples to flow acrosssaid first and said second sensor surface wherein the fluid samplescomprise a solvent at known concentration, a a measuring device formeasuring changes of refractive index at the first and second sensorsurface during the flow of each fluid sample, a processor operable todetermine a response value and a reference-subtracted response value foreach fluid sample based on said changes and creating a data setcomprising said values, each fluid sample forming a point in the dataset and for selecting a reliable set comprising at least five samplesfrom the data set, plotting the response value against thereference-subtracted response value for the reliable set and fitting acurve to them, the processor being further operable to carry out stepsa)-f) below, said steps being performed in alphabetical order for everyother fluid sample in the data set: a) calculating leverages h_(i), b)labelling points with h_(i)>h_(i) ^(cut) as outliers, and if the numberof outliers, no, is less than n_(o) ^(max)=min(n−p−1, floor((n−1)/2)),continue; otherwise, go to step f) below, c) forming a clean set withany-outliers removed and calculating n^(clean) Studentized residualst_(i) ^(ext) using a regression based on this clean set, where n^(clean)represents size of the clean set, d) labelling points with t_(i)^(ext)>t(a/(2n^(clean)), n^(clean)−p−1) as outliers, and if n_(o)<n_(o)max, continue; otherwise, go to step f) below, e) forming a clean setwith outliers removed again, if outliers were found in previous step d);if χ²>χ² _(cut), where χ² is calculated from regression of the cleanset, calculating the n^(clean) Studentized residuals t_(i) ^(ext) forall points in the clean set and labelling outliers just as was done inprevious step d), f) if any high-leverage outliers were detected in stepb) and n_(o)≤n_(o) ^(max), calculating t_(i) ^(pred) for thesehigh-leverage points using a regression based on the clean, outlier-freeset, and removing the outlier label for these points if t^(red)<t(α/2,n^(clean)−p), thereby improving the evaluation of an interaction betweenan analyte in a fluid sample and a ligand immobilized on a sensorsurface of a biosensor.